The purpose of a resonator is to provide resonant amplification for particular frequencies. Within a particular spectral region, the position of these resonances can be characterized by the absolute position of a spectral line and also by the spacing of neighboring spectral lines. Controlling the position of these resonances is of importance, in particular, in the field of short and ultra-short pulses and in frequency comb technology.
In particular, for applications using such resonators in the field of ultra-short laser pulses, the position of the resonances is often characterized by two values, the spacing of the resonance lines previously referred to, which corresponds to the pulse repetition rate of pulses circulating in such a resonator, and the so-called carrier envelope frequency, which indicates the spacing of the smallest resonance line to zero when continuing the resonances with constant spacing towards smaller frequencies. The significance of the carrier envelope frequency results from the use of such a resonator for the generation and/or filtering of regular laser pulses or of an associated frequency comb.
FIG. 1a illustrates regular laser pulses in a plot of the electric field versus time. There are shown both the envelope of the laser pulses 110 and the carrier wave 120 of the laser pulses 110. The carrier wave 120 can be represented by a sinusoidal oscillation in the range of optical frequencies.
FIG. 1b illustrates the frequency comb associated with the laser pulses 110 of FIG. 1a. This frequency comb includes a plurality of laser modes fm being spaced apart from each other by frep. Here frep is the spacing of neighbouring modes of the frequency comb. The modes fm of the frequency comb may be expressed, as mentioned above, by the following formula:fm=m×frep+f0.  (1)Here, m is a natural number. Naturally, the modes of a real frequency comb extend across a finite width in the frequency domain. The parameter f0 of the frequency comb is referred to in the following as (carrier envelope) offset frequency or carrier envelope offset frequency of the frequency comb. The presence of this offset frequency f0 resides in the fact that the frequencies of the laser modes fm are not necessarily multiples of each other. In order to adjust or otherwise control the modes fm of a resonator, in particular the modes of a frequency comb generator, it is advantageous if the spacing between neighbouring modes frep and/or the offset frequency f0 are adjustable.